P(c)=-12c^2+120c

Solution for P(c)=-12c^2+120c equation:

(P)=-12P^2+120P

We move all terms to the left:

(P)-(-12P^2+120P)=0

We get rid of parentheses

12P^2-120P+P=0

We add all the numbers together, and all the variables

12P^2-119P=0

a = 12; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·12·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*12}=\frac{0}{24}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*12}=\frac{238}{24}
=9+11/12
$